Question

Triangle A B C is shown. The length of A C is 8 and the length of C B is a. Angle C A B is 45 degrees and angle A B C is 77 degrees.

Complete the work to determine the value of a.

Use the law of sines: StartFraction sine (uppercase A) Over a EndFraction = StartFraction sine (uppercase B) Over b EndFraction.
Substitute: StartFraction sine (45 degrees) Over a EndFraction = StartFraction sine (77 degrees) Over 8 EndFraction .
Cross multiply: 8sin(45°) = asin(77°).
Solve for a and round to the nearest hundredth:
a ≈
.

Answer 1

approximately 4.75 units

Explanation:

Using the law of sines, we have:

sin(A)/a = sin(B)/b

Substituting the given values, we get:

sin(45°)/a = sin(77°)/8

Solving for 'a', we have:

a = sin(45°) * 8 / sin(77°)

a ≈ 4.75 (rounded to two decimal places)

Therefore, the length of CB is approximately 4.75 units

Answer 2

Answer:5.81

Step-by-step explanation: I'm doing the assignment rn and got it right.